Haïm Brezis, Petru Mironescu

Research output: Chapter in Book/Report/Conference proceedingChapter


We revisit the notion of topological degree deg f (aka index or winding number) for maps f: S1→ S1. This is a classical concept when f is continuous: deg f counts “how many times f(S1) covers S1, taking into account algebraic multiplicity.” One can still give a robust definition for deg f when f belongs merely to VMO(S1;S1), and thus, by the Sobolev embeddings, for maps in the critical spaces W1/p,p(S1; S1), with 1 < p< ∞. We establish some basic properties of this degree.

Original languageEnglish (US)
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
Number of pages42
StatePublished - 2021

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mechanics
  • Mathematical Physics
  • Control and Optimization
  • Applied Mathematics


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